Sangakkara, who scored 124 runs on Wednesday against Scotland, became the first batsman to score hundreds in four consecutive one-day internationals. He combined with Tillakaratne Dilshan (104) in a 195-run, second-wicket partnership as Sri Lanka posted 363-9 on the way to a 148-run win.
"Sometimes things just fall into place, everything clicks," Sangakkara said while accepting man-of-the-match honours at Hobart, Australia.
"It's difficult to pinpoint it. Maybe it's because I'm making a lot of better decisions, the right decisions at the right time, taking risks at the right time, being more calculated, being a bit more positive. I don't know what that one thing is, but whatever it is, it's working for me at the moment, and I'd like to hold on to that for as long as I can."
Sri Lanka completed its pool games with a 4-2 record, and looks like it will face South Africa in the quarterfinals next week in Sydney. Sri Lanka won the World Cup in 1996, and lost the finals in 2007 to Australia and in 2011 to India.
Sangakkara also passed Adam Gilchrist (52) at the top of the list of most dismissals by a wicketkeeper in World Cup matches, with 54. He also passed 500 ODI dismissals.
He earned the praise of his teammates after the match.
"It is a great experience to play with Kumar," Dilshan said. "I hope we can continue to bat as long as possible together, and keep on producing the big partnerships."
Opener Lahiru Thirimanne was equally as effusive.
"We are all privileged to share the same dressing room with him," Thirimanne said. "It is fantastic he is playing so wonderfully at the moment, and hopefully he continues his form in the quarterfinals."
Scotland lost opener Kyle Coetzer, caught and bowled by Lasith Malinga, on the second ball of the innings, and never threatened to win its first World Cup match in 13 attempts. The Scots were bowled out for 215 runs in the 44th over. Freddie Coleman (70) and captain Preston Mommson (60) put on a fourth-wicket century partnership in the only bright spot for Scotland.
On Thursday, South Africa plays the United Arab Emirates at Wellington, New Zealand, and skipper AB de Villiers says his team must win its final Pool B match to be assured of making the quarterfinals.
Second-place South Africa has been inconsistent so far, twice scoring 400-plus runs in big wins over the West Indies, Zimbabwe and Ireland, but losing to India and Pakistan.
A win against bottom-place UAE would all but guarantee South Africa a second-place finish in Pool B behind India. Should it suffer a major shock, South Africa would likely finish pool play in a three-way tie on six points, but would be favoured to progress thanks to a superior net run rate.
"It's a must-win for us, very important," de Villiers said. "We'd really like to get to eight points and make sure we finish second in the group."
The 42-game preliminary round ends on the weekend. New Zealand, Sri Lanka, Australia and Bangladesh have clinched quarterfinal places in Pool A. India, with five consecutive wins, is guaranteed a first-place finish in Pool B ahead of its final pool match against Zimbabwe in Auckland on Saturday.
Pakistan and Ireland, who meet in Adelaide, Australia, on Sunday, are in third and fourth place, respectively. The West Indies, in fifth place and finishing against UAE, could still advance.